Discrete Math

Definition of even:

an integer n is even if n = 2a for some integer a

Definition of odd:

an integer n is odd if n = 2a + 1 for some integer a

Definition of same and opposite parity

two integers have the same parity if they are both even or both odd. two integers have opposite parity otherwise.

What does a | b mean. Identify the divisor and the multiple.

a divides b such that b = ac for some integer c.
a is a divisor of b

b is a multiple of a

Definition of prime number

A number n is prime if it has two positive divisors, 1 and n. otherwise it is composite

what does gcd(a,b) mean

it indicates the greatest common divisor of integers a, b

what does lcm(a,b) mean?

the least common multiple of a,b

What is the division algorithm?

Given integers a,b with b > 0. There exists unique integers q and r for which a = qb + r and 0 <= r <b.

What type of statements should direct proof be considered for?

conditional statements

What type of statements should contrapositive proof be considered for?

conditional statements

Consider P => Q. How do you represent the contrapositive form of the statement?

~Q => ~P

a = b (mod n)

(a-b) % n = 0

Definition of rational

a real number is x is rational if x = a/b for some integers a,b

Definition of irrational

A real number x is irrational if x ≠ a/b for every integer a,b